Question

A national news channel reported that there is no difference between the average earnings of women and men in computer and mathematical occupations in the United States. To test this claim, we selected a team from our ECON 3100 class who gathered and looked at data from a random sample of 2500 women in computer and mathematical occupations in the King County area. The study found the average earnings of the random sample to be $75,000/year, with a sample standard deviation of $9,500. Answer the following:

a. If we know that the average earnings of men are $89,000/year, set up the null and the alternative hypotheses that the average earnings of women match the average earnings of men in the population.
b. Compute the test statistic. (Name it correctly)
c. Sketch a graph of the appropriate distribution, showing the test statistic and the critical value, if the significance level is 5%.

Answer 1

Explanation:

sample size ( n ) = 2500 women ( computer and mathematical occupations )

Average earnings of sample ( X )= $75000 / year

standard deviation ( s )= $9500

a) knowing that the average earnings of men are $89,000/year, the null and the alternative hypotheses that the average earnings of women match the average earnings of men in the population.

Given ; Ц = $89000

Null hypothesis ( H0) : Ц = $89000

Alternative hypothesis ( H1 ) : Ц ≠ $89000

The test is : one sample t test hypothesis

b) Test statistic

Test statistic ( t ) =